Simple and practical DIQKD security analysis via BB84-type uncertainty relations and Pauli correlation constraints

Michele Masini, Stefano Pironio, and Erik Woodhead

Laboratoire d'Information Quantique, Université libre de Bruxelles (ULB), Belgium

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According to the entropy accumulation theorem, proving the unconditional security of a device-independent quantum key distribution protocol reduces to deriving tradeoff functions, i.e., bounds on the single-round von Neumann entropy of the raw key as a function of Bell linear functionals, conditioned on an eavesdropper's quantum side information. In this work, we describe how the conditional entropy can be bounded in the 2-input/2-output setting, where the analysis can be reduced to qubit systems, by combining entropy bounds for variants of the well-known BB84 protocol with quantum constraints on qubit operators on the bipartite system shared by Alice and Bob. The approach gives analytic bounds on the entropy, or semi-analytic ones in reasonable computation time, which are typically close to optimal. We illustrate the approach on a variant of the device-independent CHSH QKD protocol where both bases are used to generate the key as well as on a more refined analysis of the original single-basis variant with respect to losses. We obtain in particular a detection efficiency threshold slightly below 80.26%, within reach of current experimental capabilities.

Device-Independent Quantum Key Distribution (DIQKD) protocols allow, by exploiting the phenomenon of quantum nonlocality, two users to establish a secret key even when using quantum devices that they do not trust. We provide a new and versatile approach to compute lower bounds on the key rate of two-input/two-output DIQKD protocols (a family of DIQKD protocols that require only pairs of qubits for their implementation). We apply our method to different protocols, obtaining new results in terms of noise and photon loss tolerance.

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Cited by

[1] D. P. Nadlinger, P. Drmota, B. C. Nichol, G. Araneda, D. Main, R. Srinivas, D. M. Lucas, C. J. Ballance, K. Ivanov, E. Y. -Z. Tan, P. Sekatski, R. L. Urbanke, R. Renner, N. Sangouard, and J. -D. Bancal, "Experimental quantum key distribution certified by Bell's theorem", Nature 607 7920, 682 (2022).

[2] Lewis Wooltorton, Peter Brown, and Roger Colbeck, "Tight Analytic Bound on the Trade-Off between Device-Independent Randomness and Nonlocality", Physical Review Letters 129 15, 150403 (2022).

[3] Víctor Zapatero, Tim van Leent, Rotem Arnon-Friedman, Wen-Zhao Liu, Qiang Zhang, Harald Weinfurter, and Marcos Curty, "Advances in device-independent quantum key distribution", arXiv:2208.12842.

[4] Karol Łukanowski, Maria Balanzó-Juandó, Máté Farkas, Antonio Acín, and Jan Kołodyński, "Upper bounds on key rates in device-independent quantum key distribution based on convex-combination attacks", arXiv:2206.06245.

[5] Federico Grasselli, Gláucia Murta, Hermann Kampermann, and Dagmar Bruß, "Boosting device-independent cryptography with tripartite nonlocality", arXiv:2209.12828.

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